»Is the info in The Animatrix correct?«

Isn`t The Animatrix created by other people than "the brothers". (i cant spell their last name. )

But is the information and the story approved by the brothers, or is it just theories of other people?

"Animatrix" and "Enter The Matrix" are canon, that means that they are approved to not collide with the Matrix universe, but to add to the universe

The Wachowskis are credited as writers for
Kid's Story
Second Renaissance Part 1
The Second Renaissance Part 2
Final Flight of the Osiris

and

Enter the Matrix

Some of the films in the Animatrix (namely Renisance) which are apparently taken from the Zion archives. If Zion is really an extension of the matrix, ie another virtual world, then who can say what is true and what is a lie?

Deciect by the machines is one of the many underlying themes in the matrix.